Dynamic Behavior and Buckling Analysis of Thin Rectangular Plate Rotating around Its Symmetrical Axis

A nonlinear dynamic model of thin rectangular plate rotating around its symmetrical axis with two opposite simply-supported edges and two opposite free edges is established using general Hamilton's Variational Principle. Three lower modes and the critical bifurcation values of the plate are analyzed approximately by employing assumed modes method. The results show that the overall motions can result in dynamic softening in the flexible multi-body system. Furthermore, the same method is also used to investigate the post-buckling behaviour of the plate. The symmetrical stable post-buckling solutions which are developed from the trivial solution through first bifurcation, the asymmetrical stable post-buckling solutions which are developed from the symmetrical post-buckling solutions through the second bifurcation and the antisymmetry unstable post-buckling solutions which are developed from the trivial solution through its second bifurcation are obtained.